Welcome to the .375 350gr SMK

[LouBoyd]

That must be a new bullet from Sierra. It's not in my Quckload database. Could you post it's important dimensions for handloading? Those would be:
Overal length
shank length
boattail length
boatail diameter.
Has Sierra stated it's G1 BC? I'd expect it to be close to the 300 grain 338 SMK. It would deliver 16% more energy at the same velocity just because of the added mass.

I haven't seen this bullet before but I've looked at what could shoot the 375 330 grain Lehghs subsonic and concluded that they would work nicely in a bolt action using a cartridge like a 7mm BR but with a .375 neck. It would probably be easiest to make by necking down 308 brass, The shoulder would only be .06" larger than the neck, but that's plenty. I'd expect that to be good for the 350 SMK too.

Dies would only requre reaming the neck area of a 7mmBR die to .400 +/- and using a 375 expander ball.

A custom chamber reamer might be requried but I thnk it could be chambered using a 7mm BR reamer with an overside pilot (or a solid pilot in a well aligned lathe) to cut the shouilder followed by a 375 Win Reamer to cut the throat and neck.

The 375 WIn cartridge has 48 grains capacity compared to about 41 for a 378-7mmBR and about the same pressure rating. The smaller capacity should give a little better velocity consistancy. The other advantage of the 7mm BR is it's shorter and uses a 308 size boltface. To me it sounds like a good use for a 30-06 or 270 mid length Win 70 or similar requiring no modifications other than a barrel change. I'm not sure with the Sierra 350 SMK but I don't think 375-7mmBR with the 330 grain Lehighs will fit in a 2.8" or even a 3.0" short action.